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ITEC 352

ITEC 352. Lecture 2 Low level components. Review. Electricity Math Components. Foundation. Wires Why are they coated with rubber? Crossing wires are not connected Terminated are Curved bump is not connected Represented as . Not. Symbol that implies the inverse

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ITEC 352

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  1. ITEC 352 Lecture 2 Low level components

  2. Review • Electricity • Math • Components

  3. Foundation • Wires • Why are they coated with rubber? • Crossing wires are not connected • Terminated are • Curved bump is not connected • Represented as

  4. Not • Symbol that implies the inverse • Add a circle before a connection on a diagram…

  5. Transistor • Critical piece of technology • Faucet analogy • Not gate

  6. Gates • Not Bill • Graphical representation of groups of transistors • And gate (Just like && in programming)

  7. Or / Not • Symbols Nor Xor Or Xnor

  8. Hardware • Not all hardware is constructed equally • Some is easier than others • Can construct all logic using limited set of gates (and/or/not, NAND) • NAND gates • Easiest / cheapest to produce • Problem • We don’t naturally think in NAND gates

  9. Math • DeMorgan’s Theorem Not (P and Q) = (Not P) or (Not Q) Not (P or Q) = (Not P) and (Not Q)

  10. Idempotence • Fancy word, simple concept • And a value, what do you get? • Or a value what do you get? • Useful for translating one gate type to another

  11. Others • Distributive • Associative A and (B or C) = (A and B) or (A and C) A or (B and C) = (A or B) and (A or C) A and (B and C) = (A and B) and C A or (B or C) = (A or B) or C

  12. Others • Absorption • Consensus A and ( A or B) = A A or (A and B) = A (A and B) Or (Not A and C) Or (B and C) = (A and B) Or (Not A and C) (A or B) and (Not A or C) and (B or C) = (A or B) and (Not A or C)

  13. Process • Transformation Using DeMorgan’s Law: A or B => Not ( Not (A + B) ) Not ( Not (A and B) )

  14. Tedious • Not difficult, just requires patience and practice • Practice • Turn an AND gate into NAND gates ???

  15. Answer Note: We need to invert the answer So and it with itself and invert it again

  16. Why? • Adding binary numbers • What all do we have to consider for adding 2 numbers together? • How do we represent this using gates?

  17. Summary • Transistors • Wires • Gates • Math • Example of why we learn about them

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